
where \(r_{\text{th}}\)  is the threshold radial and \(\lambda \in (0,1)\)  specifies the rate at which we suppress the high frequency zone. In this way, initial sample and noises \(\lbrace \mathbf {\eta }_t\rbrace _{t=1}^{T}\)  all exhibit a similar frequency distribution as general images,
i.e., target distribution awareness.
Besides, considering that the high-frequency details are most challenging to learn [1]}, [2]},
suppressing their amplitude implies some reduction in the generative task difficulty.
For more fine-grained regulation, we can design multiple zones each with a dedicated suppressing rate.
Without expensive grid search, we find it is empirically easy to tune the parameters based on the statistics of the natural images and the samples generated by the vanilla SGMs in the frequency domain (see Sec. REF  in Appendix for more details).
